Rigidity and Realizability for Tropical Curves in Dimension 3
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912242484641792 |
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| author | Hicks, Jeff |
| author_facet | Hicks, Jeff |
| contents | We present an unobstructedness criterion for Lagrangian threefolds $L\subset X^A$ using the $H_1(L)$-class associated with the boundary of a pseudoholomorphic disk.
As an application, let $X^A\to Q$ be a Lagrangian torus fibration whose base $Q$ is a tropical abelian threefold. Given $V\subset Q$ a rigid tropical curve with a pair-of-pants decomposition, we prove that the Lagrangian lift $L_V\subset X^A$ is unobstructed.
Provided that an appropriate homological mirror symmetry statement holds, this implies the existence of a realization $Y_V$ in the mirror abelian threefold $X^B\to Q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16582 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity and Realizability for Tropical Curves in Dimension 3 Hicks, Jeff Symplectic Geometry Algebraic Geometry 53D40, 14T20 We present an unobstructedness criterion for Lagrangian threefolds $L\subset X^A$ using the $H_1(L)$-class associated with the boundary of a pseudoholomorphic disk. As an application, let $X^A\to Q$ be a Lagrangian torus fibration whose base $Q$ is a tropical abelian threefold. Given $V\subset Q$ a rigid tropical curve with a pair-of-pants decomposition, we prove that the Lagrangian lift $L_V\subset X^A$ is unobstructed. Provided that an appropriate homological mirror symmetry statement holds, this implies the existence of a realization $Y_V$ in the mirror abelian threefold $X^B\to Q$. |
| title | Rigidity and Realizability for Tropical Curves in Dimension 3 |
| topic | Symplectic Geometry Algebraic Geometry 53D40, 14T20 |
| url | https://arxiv.org/abs/2502.16582 |